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If marginal costs fall in the gap of the MR curve P* will remain the profit maximizing price and Q* will be the profit maximzing output.
One of the points of the kinked demand curve model was that it provided an explanation for a behavior that economists were well aware of within oligopoly. It had been observed that firms in oligopolistic industries didn't change price and output often, even when production costs were known to have changed.
It turns out that this simple bit of strategic thinking on the part of firms in an oligopoly was able to explain this otherwise strange phenomenon, strange because all our models have shown that profit maximizing firms will change price and output when variable costs change.
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